The scattering of identical nuclei at low energies exhibits conspicuous Mott oscillations which can be used to investigate the presence of components in the predominantly Coulomb interaction arising from several physical effects. It is found that at a certain critical value of the Sommerfeld parameter the Mott oscillations disappear and the cross section becomes quite flat. We call this effect Transverse Isotropy (TI). The critical value of the Sommerfeld parameter at which TI sets in is found to be $eta_{c} = sqrt{3s +2}$, where $s$ is the spin of the nuclei participating in the scattering. No TI is found in the Mott scattering of identical Fermionic nuclei. The critical center of mass energy corresponding to $eta_c$ is found to be $E_c$ = 0.40 MeV for $alpha + alpha$ (s = 0) , 1.2 MeV for $^{6}$Li + $^{6}$LI (s = 1) and 7.1 MeV for $^{10}$B + $^{10}$B (s = 3). We further found that the inclusion of the nuclear interaction induces a significant modification in the TI. We suggest measurements at these sub-barrier energies for the purpose of extracting useful information about the nuclear interaction between light heavy ions. We also suggest extending the study of the TI to the scattering of identical atomic ions.
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